Yes. I just got a reply from Double-Alpha Academy (Mr. Bullet Feeder). They said that their bullet feeder will work and only requires a station in the tool head. I would need to combine the crimp and seating into one station. Lee's Custom 5.7x28mm 2-die set should do that nicely.

So, the only thing now is which caliber would work best on the case feeder side for the 5.7x28mm. I'm inclined to think the .38/.357 might work but, I differ that to brighter minds than mine to answer that question.

According to Wikipedia, the case length for the 5.7 is: 28.83 mm (1.135 in). The same web site states the .38 Special is: 1.155 in (29.3 mm).

With this in mind, I would think that there is only -0.02 in difference between the two rounds. Not enough to be a problem since this same case feeder works with the .357 Magnum, which is 1.29 in (33 mm) or 0.135 in longer than the .38.